The shocking incident, which was caught on video, reportedly happened around 6:45 p.m. on June 18 on Sheridan Avenue in the Claremont neighborhood.
The video shows the 24-year-old victim running and then tripping over the two children as the gunman runs up and starts shooting, hitting the man in the back.
The victim attempts to climb off of the children as the gunman runs up and starts shooting him in the legs.
Police say the gunman then hopped onto a scooter operated by a second suspect and both fled the scene heading northbound on Sheridan Avenue.
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The victim was taken to a nearby hospital and is listed in stable condition. Neither of the children were hurt.
Anyone with information in regard to this incident is asked to call the NYPD's Crime Stoppers Hotline at 1-800-577-TIPS (8477) or for Spanish, 1-888-57-PISTA (74782). The public can also submit their tips by logging onto the CrimeStoppers website at WWW.NYPDCRIMESTOPPERS.COM or on Twitter @NYPDTips.
Police say all calls are strictly confidential.